Physics Optics: Refraction

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PhysicsOptics Refraction
a place of mind
FACULTY OF EDUCATION
Department of Curriculum and Pedagogy

• Science and Mathematics Education Research Group

Supported by UBC Teaching and Learning
Enhancement Fund 2012-2014
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Refraction
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Refraction I
What physical phenomenon is responsible for what
you see in this photo?

1. Reflection
2. Refraction
3. Magnification
4. Reduction
5. Projection

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Solution
Answer B Justification Pencils do not bend in
water. However, looking at this glass from the
outside, the pencil appears to be bent. In order
for us to see the pencil, it has to be
illuminated by external light. The light that
reflects of the bottom half of the pencil travels
first through water and then through air. As
light crosses the boundary between these two
media (plural for medium) it bends. This
phenomenon is called refraction. This
refraction of light creates the appearance of a
bent pencil as shown in the figure.
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Refraction II
Consider this image of a pencil in a glassof
water. Why does the pencil appear bent?

1. Light reflecting off the pencil refracts as it
   travels from water to air
2. Light reflecting off the pencil disperses as it
   travels from water to air
3. The pencil loses structural integrity and bends.
4. Light emitted by the pencil refracts as it
   travels from water to air.

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Solution
Answer A Justification Pencils do not bend in
water. However, looking at this glass from the
outside, the pencil appears to be bent. In order
for us to see the pencil, it has to be
illuminated by external light the pencil is not
a light source and does not emit light.
Dispersion of light occurs because the index of
refraction of light depends on the colour
(frequency) of the light. Think about how
rainbows are created The light that reflects of
the bottom half of the pencil travels first
through water and then through air. As light
crosses the boundary between these two media it
bends (refracts). This refraction of light
creates the appearance of a bent pencil as shown
in the figure.
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Extend Your Learning Video
Title The Science of Rainbows
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Fermat Principle
Fermats principle A light ray propagating
between any two points always takes the path it
can traverse in the least amount of time.
Because light travels at different speeds in
different media, when light travels across a
boundary from one medium to another, the
direction of travel may change. Least distance
is not the same as least time unless the medium
doesnt change.
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Refraction III
Refraction occurs because

1. Light travels at different speeds in different
   media
2. Light obeys different laws in different media
3. Light never travels along a straight line
4. Light always follows the path of least distance

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Solution
Answer A Justification Fermats principle
states that light travels along the path of least
time. Light also travels at different speeds in
different media (materials), but always obeys the
same laws. When light travels from one medium to
another, the speed of light changes, and the path
is adjusted to continue to follow the path of
least time.
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Refraction IV
The angle of refraction

1. Is always equal to the angle of incidence
2. Is always greater than the angle of incidence
3. Is always less than the angle of incidence
4. May be greater than, less than, or equal to the
   angle of incidence

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Solution
Answer D Justification Unlike the law of
reflection, the angle of incidence and refraction
are not always equal. This is because the light
is not always travelling in the same material,
and so the speed of light changes, and the path
adjusts to follow the path of least time. The
angle of refraction can be greater than, less
than, or equal to the angle of incidence.
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Refraction V
The angle of refraction depends on

1. The index of refraction of the incident medium
2. The index of refraction of the refracting medium
3. The indices of refraction of both media

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Solution
Answer C Justification As we discussed in the
previous question, the angle of refraction can be
greater than, less than, or equal to the angle of
incidence. This is because the light is not
always travelling in the same material, and the
speed of light changes. Light always follows the
path of least time, not distance, so when the
speed changes the direction must also change.
Depending on the refractive indices of the media
on each side of a boundary, the angle of
refraction can be greater than, less than, or
equal to the angle of incidence.
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Refraction VI
A ray of light travels from air into a block of
glass. Identify the angle of refraction.
The normal is represented by a dashed line.
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Solution
Answer D Justification Think about the law of
reflection, and how the incident and reflected
angles are measured. In a situation involving
refraction, the incident and refracted angles are
measured in the same way as a situation involving
reflection between the normal and the ray. In
this situation, B is the angle of
incidence(measured between the normal and
theincident ray), and D is the angle of
refraction (measured between the normal and the
refracted ray).
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Refraction VII
A ray of light travels from air towards glass at
an angle (red). At the interface, the ray

1. Is totally reflected
2. Is bent away from the normal
3. Does not bend
4. Is bent toward the normal
5. Bends across the normal

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Solution
Answer D Justification Light travels more
slowly in glass than it does in air. As a result,
the light will bend towards the normal when it
crosses the boundary between the two materials.
Think about driving a car from pavement to gravel
at an angle. When the first wheel hits the
gravel, it will move slower than the others still
on the pavement. Because the outside wheels are
turning faster, the car will turn toward the
first wheel, and the path bends toward the
normal.
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Extend Your Learning Activity
The light ray A group of students forms two
straight lines (standing shoulder to
shoulder).Each pair connects themselves using
meter sticks. The media A strip of masking tape
divides the room into two media. In one of the
media (on one side of the tape), students walk at
a normal pace. In the other media (or on the
other side of the tape), students walk very
slowly using baby steps. Refraction The group
of students walk forward together in a straight
line towards the diagonal strip of masking tape.
The students maintain the line as they approach
the masking tape. When an individual student
reaches the tape, that student abruptly changes
the pace of her/his walk. The group of students
continues walking until all students in the line
have entered into the second medium. 
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Refraction VIII
A light ray travels from medium A into medium B
as shown. This means that

1. Light travels faster in B than in A
2. Light travels faster in A than in B
3. A is less optically dense than B
4. B has a higher index of refraction than A
5. All of the above

Medium A
Medium B
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Solution
Answer A Justification The faster light
travels in a given medium, the further the ray
bends away from the normal line at the boundary.
The angle of refraction in B is larger than the
angle of incidence in A. This is because light
is travelling faster in medium B. The speed of
light in a medium is related to its optical
density, and thus its index of refraction. The
more optically dense a medium, the slower the
light travels, and the larger the index of
refraction. Because light travels more slowly in
A, we know that A is more optically dense than B,
and thus has a higher index of refraction. Think
about the example of the car. What happens to the
wheels when the car travels, at an angle, from
gravel to pavement?
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Solution continued
Extended explanation Light travels at the speed
of light 3108 m/s in a vacuum. The speed of
light is reduced when it goes from a less
optically dense medium (vacuum) to a more
optically dense medium. We can think of a more
optically dense medium having more atoms that the
light has to bounce off of as opposed to having
nothing that obstructs its motion like in a
vacuum less obstruction less speed impedance.
Optic density can be measured by the index of
refraction (n). A higher optic density would mean
a higher index of refraction. We can now relate
the speed of light (v) in a medium with index of
refraction (n) n c/v where c is the speed of
light in a vacuum. Using this relationship we see
that the greater the index of refraction, the
slower the speed of light is in the medium.
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Refraction IX
water
Light travels through water into air. The angle
of refraction will be
air

1. Less than the angle of incidence
2. Equal to the angle of incidence
3. Greater than the angle of incidence

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Solution
Answer C Justification When light travels
from a medium with a high refractive index to one
with a low refractive index, light bends away
from the normal. When light travels from a
medium with a low refractive index to one with a
high refractive index, light will bend towards
the normal. When light travels in the same
medium, the speed of light does not change, no
refraction occurs, and the angle of incidence and
refraction are equal. Water is more refractive
than air, so the light will bend away from the
normal.
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Refraction X
Light travels from air, through a glass block,
and exits into air. The angle of refraction of
the ray as it exits the block is

1. Less than angle of incidence at entrance point
2. Less than angle of incidence at exit point
3. Equal to angle of incidence at entrance point
4. Greater than angle of incidence at entrance point
5. Not enough information

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Solution
Answer C Justification When light travels from
material A to B, light bends according to Snells
Law. When light travels back across the
boundary, the light bends (again) according to
Snells Law. These equations are identical,
implying that light behaves in an equal, but
opposite, manner when it travels from A to B, and
then B to A. The angle of incidence entering the
block is equal to the angle of refraction leaving
the block.
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Refraction XI
A light ray travels from a given medium into
three different media at the same angle of
incidence. Rank the media's indices of
refraction from greatest to least.

1. nA nB nC
2. nB gt nC gt nA
3. nA gt nC gt nB
4. nA gt nB gt nC
5. nC gt nA gt nB

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Solution
Answer C Justification To determine the
relative refractive indices of medium A, medium
B, and medium C, we have to look at the angle of
refraction in each. In each situation, the light
is incident at the same angle, from the same
medium. This means we can directly compare each
situation.   Mathematically, since the initial
medium and the angle of incidence are the same
for all three media Snells Law So
as ?R decreases, sin?R decreases, and nR must
increase to maintain the constant ratio of
Snells Law. The smaller the angle of refraction,
the larger that medium's refractive index.
Remember ?R lt 90
Solution is continued on the next slide
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Solution Contd
Medium A has the smallest angle of refraction and
the largest index of refraction. Medium B has the
largest angle of refraction and the smallest
index of refraction. Medium C falls in the
middle.
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Refraction XII
A light ray travels through a vacuum and into a
mystery medium. Which of the following diagrams
could accurately represent a possible scenario
for this system?
I II III

1. Case I
2. Case II
3. Case III
4. Cases I and II
5. Cases I and III

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Solution
Answer E Justification The refractive index
of a vacuum is 1.  Light travels slower in every
other medium, so every other medium must have an
index of refraction greater than 1. When light
travels from one medium to a medium with a larger
index of refraction, the light ray bends toward
the normal.   Case I passes this test, case II
does not, and case III causes the light to travel
straight through with no bending". Because the
light does not bend as it travels into the
mystery medium in Case III, we know that in that
case, the mystery medium must be a vacuum. Case
II shows a light ray bending away from the
normal. This would mean that light
travels faster in the mystery medium than it does
in a vacuum. This is not possible, thus case II
will never happen.
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Snells Law
We know that light bends when it travels from one
medium into another. But how much does it bend?
Snells Law tells us how the incident and
refracted rays are related, using the refractive
indices of the two media. On the left hand
side is the incident material. The refracting
material is on the right.
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Extend Your Learning Video
Title Snells Law Song
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Extend Your Learning Video
Title Invisible Glass How to make an object
disappear
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Refraction XIII
A light ray travels from air, into a glass block,
and out the other side. In the first experiment,
the block is made of flint glass (n 1.66). In
the second experiment, the block is made of crown
glass (n 1.5). Lateral displacement of light
traveling through the flint glass block is

1. Less than the crown glass block
2. Greater than the crown glass block
3. Equal to the crown glass block

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Solution
Answer B Justification The more refractive a
material is, the more the refracted ray will bend
towards the normal. Flint glass is more
refractive than crown glass, so the refracted ray
will bend more towards the normal in the flint
glass than the crown glass. Bending more towards
the normal means the ray is bending further from
the original path of the light ray. When the ray
refracts out of the block, the refracted ray
will be parallel to the original, incident ray.
Lateral displacement is the distance between
these two rays.
crown
flint
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Refraction XIV
A ray of light passes through a wedge of glass
(ng 1.5) as shown. The wedge is surrounded by
air (na 1). In which approximate direction is
the ray travelling after leaving the wedge?
Position of ray along exit edge is not accurate.
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Solution
Answer A Justification When the light ray
enters the wedge, it is refracted towards the
normal because glass is more dense than air. It
is travelling upwards, relative to the
horizontal. Upon existing the second face, the
light ray bends away from the normal as air is
less dense than glass. This causes the light ray
to pointfurther up, away from the horizontal.
What if the block were made of air, and
thelight was travelling from glass to air and
back? Would the direction of the refracted light
be different?
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Refraction XV
An observer is standing on a bridge, looking
straight down into a pond full of gold fish. The
goldfish appear to be

1. Further away than they really are
2. As far away as they really are
3. Closer than they really are

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Solution
Answer B Justification The observer is looking
straight down into the pond, perpendicular to the
surface of the water. Light does not refract
when the angle of incidence is 90, so looking in
to the water is like looking through a window
the object is at its real distance. The goldfish
appear to be as far from the surface as they
really are.
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Refraction XVI
An observer is standing on the side of a pond,
looking out and down at the gold fish. The gold
fish appears to be

1. Swimming deeper in the pond
2. Swimming at their actual depth
3. Swimming closer to the surface

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Solution
Answer C Justification When light travels from
the goldfish to the eye of the observer, the
light must cross the boundary between water and
air. As the light exits the pond, it bends away
from the normal. The observer sees the fish
along this refracted line, which is above the
position of the real fish. The same phenomenon
is seen when a pencil is placed in aglass of
water.
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Refraction XVII
Light travels from air into a semicircular block.
The incident light ray is pointed directly at the
centre of the flat edge. Why is the light not
refracted upon entering the block?

1. The law of refraction only applies for straight
   boundaries
2. The radius of the block is perpendicular to the
   surface at all points
3. The light doesnt refract when it travels from
   air to glass
4. The light doesnt refract when it travels from
   glass to air
5. It is refracted, but the angle is so small that
   we do not see it

air
glass
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Solution
Answer B Justification The glass block is a
semicircle. At all points along the edge of a
circle, the radius is perpendicular to the edge.
Because the light ray travels along the radius,
it is perpendicular to the surface at the point
of contact. When light is incident on a boundary
at 0 degrees (perpendicular to the surface
remember that angle of incidence is measured from
the normal), no refraction occurs. We can test
this mathematically using Snell's Law
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Extend Your Learning Video
Title Total Internal Reflection